The only people who actually say this are the guards so its more likely that it was a rumor, Elisif never actually claimed he shouted Torygg to peices only that he used his Thu'um which in itself should be considered a act of defilement of the teachings of Kyne thus making Ulfric a heretic towards the divines.
Not really. Ulfric was not a follower of the Way of the Voice. Is the Dragonborn a heretic everytime he/she shouts at something? Heck, Jurgen Windcaller only won people over to the Way by shouting at them until they listened. An irony to be sure, but very Nord-ic all the same.
No, no he didn't have Imperial support, no where in any bits of lore was that confirmed also if Torygg was a puppet why did he agree that skyrim should be independent? That doesn't sound like something a puppet king would say, Torygg agreed with Ulfric but he said that now is not the time for it, why? Because you have a sleeping beast that still threatens all of humanity.
Official sanction? Of course not. The Empire couldn't be caught actively allowing its citizens to break the White Gold Concordat without risking open war with the Aldmeri Dominion. But you can bet dollars to doughnuts that there was some sort of shadowy figure standing behind Igmund, offering him money and promises.
The Jarls of Solitude were historically the High Kings, and were historically the most open to Imperial influence. Coincidence? I think not. Torygg may have entertained the idea of a free Skyrim, but he publicly took the opposite stance. He knew that he was High King so long as he did what the Empire wanted. As soon as he stopped, it was a knife in the dark and his "grieving" widow takes the throne, backed at the moot by Jarls like Igmund with Imperial coin in their pockets. Even Balgruuf couldn't escape the taint of Imperial money. "That's not the point," he said, but in a voice that showed he knew it didn't matter what the point was. He
had taken the money, after all.
A little off topic: Something I find funny is how the Imperial supporters claim he only have lust for the throne and the Stormcloak supporters claim he is doing it to free Skyrim. Seems there aren't that many who consider the opportunity that his motives are a mix of the two.
Obviously it was both. He wanted a free Skyrim, and he wanted to be king. The main question is, which one was the driving factor behind his rebellion. In the results, it doesn't matter much, but in the question of what kind of man he was, it is a big deal.